Slightly drunk — the happy, early stage, after one or two drinks, when you feel warm and relaxed and laugh more easily, but you can still walk and talk and think clearly enough. It is a gentle, friendly, slightly old-fashioned-sounding word, and people mostly use it about themselves or about friends, often with a smile: "I'm a bit tipsy." That softness is the point — calling someone tipsy is a kind way of saying they have had a few, where "drunk" would sound like a criticism. Because of this, people also use it to be politely dishonest about how drunk they really are. It sits on a scale that runs roughly: sober → tipsy → drunk → wasted / hammered / plastered. There is also an older, rarer use meaning "tilting, not standing straight" — a tipsy old house leaning to one side — which is where the word came from in the first place. Note that it is almost never used before a noun in ordinary speech; people say "she was tipsy", not "a tipsy woman".